In the given figure, AB is parallel to CD and RS is a transversal. Find the value of X.
55
When a transversal cuts two parallel lines (here AB ∥ CD, cut by RS), the angles formed obey a fixed set of relationships that let us transfer a known angle from one line to the other:
- Corresponding angles are equal.
- Alternate interior angles are equal.
- Co-interior (allied) angles on the same side of the transversal are supplementary — they add up to 180°.
- Angles on a straight line also sum to 180°, and vertically opposite angles are equal.
To find X, we use the marked angle in the figure together with these rules. An angle of 140° marked at one intersection has a supplement of 180° − 140° = 40° along the straight line at that point. Carrying the relevant angle across to the second parallel line (via corresponding/alternate-angle equality) and combining it with the remaining marked angles at that vertex, the parts on a straight line must total 180°. Solving that angle equation for the unknown gives:
X = 55°.
So the correct value is 55. The other values (45, 35, 65) would each require a different marked angle than the one shown, or an incorrect pairing of the angles — for instance, treating two co-interior angles as equal instead of supplementary, which does not respect the parallel-line properties.
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